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Interpreting the Helioseismic and Magnetic Imager (HMI) Multi-Height Velocity Measurements

  • Solar Cycle 24 as seen by SDO
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Abstract

The Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) filtergrams, taken at six wavelengths around the Fe i 6173.3 Å line, contain information about the line-of-sight velocity over a range of heights in the solar atmosphere. Multi-height velocity inferences from these observations can be exploited to study wave motions and energy transport in the atmosphere. Using realistic convection-simulation datasets provided by the STAGGER and MURaM codes, we generate synthetic filtergrams and explore several methods for estimating Dopplergrams. We investigate at which height each synthetic Dopplergram correlates most strongly with the vertical velocity in the model atmospheres. On the basis of the investigation, we propose two Dopplergrams other than the standard HMI-algorithm Dopplergram produced from HMI filtergrams: a line-center Dopplergram and an average-wing Dopplergram. These two Dopplergrams correlate most strongly with vertical velocities at the heights of 30 – 40 km above (line center) and 30 – 40 km below (average wing) the effective height of the HMI-algorithm Dopplergram. Therefore, we can obtain velocity information from two layers separated by about a half of a scale height in the atmosphere, at best. The phase shifts between these multi-height Dopplergrams from observational data as well as those from the simulated data are also consistent with the height-difference estimates in the frequency range above the photospheric acoustic-cutoff frequency.

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Acknowledgements

BL acknowledges support from the IMPRS Solar System School. BL computed the line profiles from the STAGGER data cubes and the response functions using the SPINOR code. We thank Michiel van Noort, Thomas Straus, and Jesper Schou for helpful discussions and comments. KN and LG acknowledge support from EU FP7 Collaborative Project “Exploitation of Space Data for Innovative Helio-and Asteroseismology” (SPACEINN). LG acknowledges support from DFG SFB 963 “Astrophysical Flow Instabilities and Turbulence” (Project A1). The HMI data used are courtesy of NASA/SDO and the HMI science team. This work was carried out using the data from the SDO HMI/AIA Joint Science Operations Center Data Record Management System and Storage Unit Management System (JSOC DRMS/SUMS). The NSO/Kitt Peak FTS data used here were produced by NSF/NSO. RS acknowledges support by NASA grant NNX12AH49G and NSF grant AGS1141921. The STAGGER calculations were performed on the Pleiades cluster of the NASA Advanced Supercomputing Division at Ames Research Center. The German Data Center for SDO (GDC-SDO), funded by the German Aerospace Center (DLR), provided the IT infrastructure to process the data.

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Authors and Affiliations

  1. Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077, Göttingen, Germany

    Kaori Nagashima, Laurent Gizon, Aaron C. Birch, Robert Cameron & Sanja Danilovic

  2. Institut für Astrophysik, Georg-August-Universität Göttingen, 37077, Göttingen, Germany

    Björn Löptien & Laurent Gizon

  3. Stanford University, Stanford, CA, 94305, USA

    Sebastien Couvidat

  4. ESA Science Operations Department, c/o NASA/GSFC, Greenbelt, MD, 20771, USA

    Bernhard Fleck

  5. Michigan State University, East Lansing, MI, 48824, USA

    Robert Stein

Authors
  1. Kaori Nagashima
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  2. Björn Löptien
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  3. Laurent Gizon
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  4. Aaron C. Birch
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  5. Robert Cameron
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  6. Sebastien Couvidat
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  7. Sanja Danilovic
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  8. Bernhard Fleck
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  9. Robert Stein
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Corresponding author

Correspondence to Kaori Nagashima.

Additional information

The Many Scales of Solar Activity in Solar Cycle 24 as seen by SDO

Guest Editors: Aaron Birch, Mark Cheung, Andrew Jones, and W. Dean Pesnell

Appendix: Conversion of the Doppler Signal Made of Pairs of Filtergrams into Doppler Velocities

Appendix: Conversion of the Doppler Signal Made of Pairs of Filtergrams into Doppler Velocities

For the calculation of the core, wing, far-wing, and average-wing Doppler velocities (Doppler velocity 1 in the list in Section 2.3), we convert the Doppler signal [D br] into the line-of-sight velocity, using the parameters that we obtain in the following manner:

  1. i)

    calculate the Doppler shift of the line core from −10 km s−1 to +10 km s−1,

  2. ii)

    shift the whole average line profile by the amount of the line-core Doppler shift, and calculate the filtergrams by convolving the shifted line profile with the filter profiles,

  3. iii)

    calculate the Doppler signals [D br] for each velocity shift, and

  4. iv)

    fit the velocity to a third-order polynomial function of D br in a certain range of the velocity.

The fitting range is chosen so that the third-order polynomial fitting seems reasonably good. Figure 17 shows how the Doppler signals change as the velocity shift changes. The fitting curves are plotted as well. Figure 17 clearly shows the saturation of the Doppler signal with the significantly large Doppler shift. This limits the range useful for the fitting.

Figure 17
figure 17

Doppler-signal changes calculated using (a) the STAGGER average line profile, (b) the MURaM average line profile, and (c) the HMI reference line profile. The data points between the solid horizontal lines are used for the fitting, and the fitted third-order polynomial functions are plotted as dots. Positive velocity indicates upward velocity, which causes a blue-shift of the line.

Full size image

The conversion parameters depend on the line profile. The line profiles obtained from STAGGER and MURaM datasets and the HMI reference line profiles are different (see Figure 1), and we calculate the fitting parameters for each line profile. For comparison, the polynomials obtained by the fitting are overplotted in Figure 18. This figure also includes scatter plots of HMI observation Doppler signals averaged over a certain field of view (see below) and the SDO line-of-sight motion towards the Sun. The observation data were obtained on 22 – 24 January 2011. The 30-degree-square quiet region near the disk center is tracked at the Carrington rate by using mtrack (Bogart et al. 2011).

Figure 18
figure 18

The third-order polynomial fits to the Doppler signals obtained by the fitting to convert the signals to the velocities (black dotted, red dashed, and green dash–dotted curves for each line profile) as shown in Figure 17. Blue lines are the SDO line-of-sight velocity plotted against the mean Doppler signals over the average of the 30-degree-square field of view near the disk center. Positive velocity indicates upward velocity.

Full size image

Note that Nagashima et al. (2013) used the spacecraft motion to compute these conversion curves. The spacecraft motion is limited to ≈ 3.5 km s−1 (Schou et al. 2012) and thus the velocity range of the fitting curve available by this method is limited. Therefore, instead, here we use the average line profiles (for STAGGER and MURaM datasets) or HMI reference profiles (for observation datasets) to obtain larger velocity ranges.

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Nagashima, K., Löptien, B., Gizon, L. et al. Interpreting the Helioseismic and Magnetic Imager (HMI) Multi-Height Velocity Measurements. Sol Phys 289, 3457–3481 (2014). https://doi.org/10.1007/s11207-014-0543-5

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  • DOI: https://doi.org/10.1007/s11207-014-0543-5

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